Tüm alıştırma soruları

Soru 4881Soru →

A search and rescue grid map uses a scale of $\frac{2}{3}\text{ inch} = 10\text{ miles}$ . If a distress beacon is located $60\text{ miles}$ away from the rescue station, what is the distance between these two points on the map in inches?

4

6

9

40

Cevabı ve açıklamayı göster

Cevap: $4$

Cevap

The distance on the map is

4

inches.

To find the map distance, first determine the scale multiplier by dividing the total actual distance by the reference distance in the scale (

60 \div 10 = 6

). Next, multiply this factor by the scale measurement on the map (

6 \times \frac{2}{3} = \frac{12}{3} = 4

). Thus, the distance on the map is exactly

4

inches.

Adım Adım Çözüm

1

Determine how many

10

-mile units fit into the total actual distance of

60

miles.

60 \div 10 = 6

units.

This establishes the scale multiplier, telling us how many times we need to apply the map's specified scale distance.

2

Multiply the scale multiplier by the map's fractional measurement.

6 \times \frac{2}{3} = \frac{12}{3} = 4

inches.

Because each

10

-mile unit represents

\frac{2}{3}

of an inch on the map, multiplying them gives the total map distance.

Anahtar Kavram

Scale Drawings and Map Measurements

Soru 4882Soru →

What is the value of the following expression?

\frac{3}{4} + \frac{1}{2} \div \frac{2}{3} - \frac{1}{8}

\frac{5}{8}

1 \frac{3}{4}

1 \frac{3}{8}

1 \frac{5}{8}

Cevabı ve açıklamayı göster

Cevap: $1 \frac{3}{8}$

Cevap

The correct answer is

1 \frac{3}{8}

.

The correct answer is found by first performing the division operation (which becomes

3/4

), then finding a common denominator (8) to add and subtract the remaining fractions. This yields

11/8

, which simplifies to

1 \frac{3}{8}

.

Adım Adım Çözüm

1

Evaluate the division portion of the expression first according to the order of operations.

\frac{1}{2} \div \frac{2}{3} = \frac{1}{2} \times \frac{3}{2} = \frac{3}{4}

The order of operations requires division to be performed before addition or subtraction.

2

Substitute the division result back into the original expression.

\frac{3}{4} + \frac{3}{4} - \frac{1}{8}

This updates the expression to contain only addition and subtraction operations.

3

Find the least common multiple (LCM) for the denominators to perform addition and subtraction.

The LCM of 4 and 8 is 8. Converting the fractions yields

\frac{6}{8} + \frac{6}{8} - \frac{1}{8}

.

Fractions must have a common denominator to be added or subtracted.

4

Perform the addition and subtraction sequentially from left to right.

\frac{6}{8} + \frac{6}{8} - \frac{1}{8} = \frac{12}{8} - \frac{1}{8} = \frac{11}{8}

Addition and subtraction carry the same precedence and are evaluated from left to right.

5

Convert the resulting improper fraction into a mixed number.

\frac{11}{8} = 1 \frac{3}{8}

The answer choices are presented as mixed numbers, requiring the improper fraction to be converted.

Anahtar Kavram

Applying the order of operations (PEMDAS) to compound fraction arithmetic.

Soru 4883Soru →

Based on the contrast context clue in the passage, determine the single word that best completes the sentence.

Aşağıdaki boşlukları doldurun

During the overhaul of the marine diesel generator, maintenance technicians observed that while the synthetic intake manifold gaskets remained remarkably supple and easily resisted tearing during disassembly, the high-heat exhaust flange seal had become completely and shattered as soon as technicians applied wrench pressure.

Cevabı ve açıklamayı göster

Cevap

brittle

The passage establishes a direct contrast using the transition word 'while'. The intake gaskets are described as 'supple' and tear-resistant, whereas the exhaust seal 'shattered' under slight wrench pressure. Therefore, the blank requires an antonym for supple, with 'brittle' precisely capturing the quality of breaking or snapping easily under stress.

Adım Adım Çözüm

1

Identify the contrast indicator and the primary clue in the passage.

The conjunction 'while' signals an opposing relationship between the intake manifold gaskets and the exhaust flange seal. The intake gaskets are characterized as 'supple' (flexible and elastic).

Contrast words establish that the two described objects possess opposite physical characteristics.

2

Determine the required antonym that aligns with the passage evidence.

The direct opposite of 'supple', supported by the fact that the seal 'shattered' when pressure was applied, is 'brittle'.

The blank must express the mechanical state of being hard but liable to break or shatter easily.

Anahtar Kavram

Identifying Antonym and Contrast Context Clues

Tahmini Süre:1m 0s

Soru 4884Soru →

A map uses a scale where $3\text{ cm}$ represents $20\text{ km}$ . If two towns are separated by $15\text{ cm}$ on the map, what is the actual distance between them in kilometers?

4

32

100

300

Cevabı ve açıklamayı göster

Cevap: $100$

Cevap

100

The correct answer is determined by setting up a direct proportion between the map distance and the actual distance:

\frac{3}{20} = \frac{15}{x}

. Cross-multiplying yields

3x = 300

. Dividing both sides by

3

isolates

x

, resulting in

100\text{ km}

. Alternatively, you can observe that the map distance increased by a factor of

5

(

3 \times 5 = 15

), so the actual distance must also increase by a factor of

5

(

20 \times 5 = 100

).

Adım Adım Çözüm

1

Identify the given scale ratio from the problem.

The ratio of map distance to actual distance is

3\text{ cm} : 20\text{ km}

.

This baseline ratio establishes the mathematical relationship needed to find any other actual distance.

2

Set up a proportion matching map measurements to actual measurements.

\frac{3}{20} = \frac{15}{x}

Keeping the units aligned (map distance in the numerator, actual distance in the denominator) ensures the proportion is solvable.

3

Solve for the unknown actual distance

x

using cross-multiplication.

3x = 15 \times 20 \rightarrow 3x = 300

Cross-multiplication transforms the proportion into a standard linear equation.

4

Isolate

x

by dividing both sides of the equation by

3

.

x = \frac{300}{3} = 100

Dividing both sides balances the equation and provides the final actual distance in kilometers.

Anahtar Kavram

Direct Proportions and Scale Factors

Soru 4885Soru →

Which of the following represents the value of $p$ that satisfies the given equation?

-2(4p - 5) + \frac{1}{3}(15p - 12) = 2p - (7p - 14)

-10

4

10

14

Cevabı ve açıklamayı göster

Cevap: 4

Cevap

4

The correct answer is 4. To solve the equation, first distribute the outer terms across the parentheses on both sides:

-2(4p - 5)

becomes

-8p + 10

,

\frac{1}{3}(15p - 12)

becomes

5p - 4

, and

-(7p - 14)

becomes

-7p + 14

. Combining like terms on the left side (

-8p + 5p

and

10 - 4

) gives

-3p + 6

. On the right side, combining

2p

and

-7p

gives

-5p + 14

. Setting these equal gives

-3p + 6 = -5p + 14

. Adding

5p

to both sides yields

2p + 6 = 14

, and subtracting 6 from both sides gives

2p = 8

. Dividing by 2 results in

p = 4

.

Adım Adım Çözüm

1

Distribute the coefficients to remove parentheses on the left side.

-8p + 10 + 5p - 4 = 2p - (7p - 14)

Applying the distributive property is necessary to eliminate grouping symbols.

2

Distribute the negative sign to remove parentheses on the right side.

-8p + 10 + 5p - 4 = 2p - 7p + 14

Distributing the subtraction over the group allows all terms to be evaluated.

3

Combine like terms on each side of the equation independently.

-3p + 6 = -5p + 14

Simplifying both sides makes it easier to balance the equation and isolate the variable.

4

Add

5p

to both sides and subtract 6 from both sides.

2p = 8

Performing these inverse operations groups all variable terms on one side and all constant terms on the other.

5

Divide both sides by 2.

p = 4

Dividing by the coefficient isolates the variable

p

, revealing its final value.

Anahtar Kavram

Solving complex multi-step linear equations using the distributive property and combining like terms.

Soru 4886Soru →

Read the following excerpt from a hangar maintenance audit:

While the initial visual inspection of the airframe was remarkably meticulous, covering every rivet and hydraulic line with painstaking care, the subsequent check of the emergency survival kit was merely perfunctory. Technicians glanced briefly at the outer seals before signing off on the inventory log without opening the container.

As used in the passage, what is the meaning of the word "perfunctory"?

Thorough and deeply detailed

Hasty and superficial

Related to emergency survival gear

Officially certified and functional

Cevabı ve açıklamayı göster

Cevap: Hasty and superficial

Cevap

Hasty and superficial

The passage uses the contrast conjunction 'While' to contrast the airframe inspection, which was 'remarkably meticulous' and conducted with 'painstaking care', with the emergency kit check, which was 'merely perfunctory'. The detail that technicians 'glanced briefly' reinforces that 'perfunctory' means carried out with minimal effort, making 'Hasty and superficial' the correct answer.

Adım Adım Çözüm

1

Identify the target word and surrounding transition signals.

The target word is 'perfunctory', introduced by the subordinating contrast conjunction 'While'.

Contrast signal words establish that two ideas or qualities in the sentence are opposites.

2

Analyze the contrasting counterpart and supporting context clues.

The airframe check is described as 'remarkably meticulous' and conducted with 'painstaking care', whereas technicians 'glanced briefly' at the seals without opening the kit.

The antonym of 'meticulous' combined with the action of glancing briefly indicates an action done with minimal effort or care.

3

Select the definition that matches the deduced contrast.

'Hasty and superficial' accurately conveys the opposite of 'meticulous' and fits the technicians' brief glance.

This directly satisfies the contrast relationship established by the passage.

Anahtar Kavram

Using contrast indicators such as 'while' to deduce the antonymous meaning of an unfamiliar word.

Tahmini Süre:1m 0s

Soru 4887Soru →

Read the three brief excerpts from naval engineering field evaluations below. Which author tone or attitude correctly matches each excerpt?

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

The excerpt evaluating the titanium-reinforced hull matches with 'Skeptical and cautionary'; the excerpt describing the autonomous sonar navigation suite matches with 'Appreciative and commendatory'; and the excerpt recording fuel consumption data matches with 'Objective and matter-of-fact'.

The author's tone is determined by analyzing descriptive word choices: the first excerpt uses qualifying words ('failed to account', 'questionable') to urge prudence; the second excerpt utilizes complimentary language ('flawlessly', 'exceptional', 'invaluable') to commend performance; and the third excerpt presents unembellished measurements ('consumed 420 liters', 'aligning directly') to deliver an unbiased report.

Adım Adım Çözüm

1

Analyze the diction in the first excerpt regarding the titanium-reinforced hull.

Identified reservations in phrases such as 'failed to account' and 'reliability questionable.'

Negative evaluative phrases and calls for caution indicate a skeptical and cautionary attitude.

2

Analyze the diction in the second excerpt regarding the autonomous sonar suite.

Identified high praise in terms like 'flawlessly,' 'exceptional precision,' and 'invaluable.'

Strongly favorable descriptive words convey an appreciative and commendatory tone.

3

Analyze the diction in the third excerpt regarding diesel-electric fuel consumption.

Identified plain quantitative statements ('consumed 420 liters', 'aligning directly with baseline parameters') without qualitative bias.

Reporting verified figures without personal opinion or emotional color denotes an objective and matter-of-fact tone.

Anahtar Kavram

Inferring Author Tone and Attitude through Diction and Phrasing

Tahmini Süre:1m 30s

Soru 4888Soru →

A logistics unit packs $3$ boxes of rations for every $4$ boxes of water. If they pack $12$ boxes of rations, how many boxes of water do they pack?

9

13

16

28

Cevabı ve açıklamayı göster

Cevap: $16$

Cevap

16

The ratio of rations to water is 3 to 4. Since the actual number of rations (12) is exactly 4 times the ratio number (3), the number of water boxes must also be 4 times its corresponding ratio number. Multiplying 4 by 4 yields 16 boxes of water.

Adım Adım Çözüm

1

Set up the proportion comparing rations to water.

\frac{3}{4} = \frac{12}{x}

This establishes the mathematical relationship between the known ratio and the actual amounts.

2

Determine the scale factor for the rations.

12 \div 3 = 4

Finding how many times the base ratio was multiplied to get the actual number of rations.

3

Apply the scale factor to the water portion of the ratio.

4 \times 4 = 16

To maintain the proportion, both parts of the ratio must be multiplied by the same scale factor.

Anahtar Kavram

Solving basic proportions by finding and applying a scale factor.

Tahmini Süre:45s

Soru 4889Soru →

A shipment contains a number of crates equal to twice the quantity of seven less than the target value, $v$ . What expression defines the number of crates?

2(v - 7)

2v - 7

2(7 - v)

7 - 2v

Cevabı ve açıklamayı göster

Cevap: $2(v - 7)$

Cevap

The correct expression is

2(v - 7)

.

The phrase 'seven less than the target value,

v

' establishes a baseline amount of

v - 7

. The problem then states we need 'twice the quantity of' that baseline amount. To multiply the entire baseline amount by two, we must enclose

v - 7

in parentheses, resulting in

2(v - 7)

.

Adım Adım Çözüm

1

Translate the phrase 'seven less than the target value,

v

'.

The expression becomes

v - 7

.

The phrase 'less than' is a turnaround phrase, meaning the seven must be subtracted from the variable

v

.

2

Translate the phrase 'twice the quantity of' and apply it to the first step.

The final expression is

2(v - 7)

.

The word 'quantity' indicates that the entire previous expression (

v - 7

) must be grouped in parentheses before multiplying by two.

Anahtar Kavram

Translating Word Phrases into Algebraic Equations

Soru 4890Soru →

Evaluate the following algebraic expression given $x = -3$ , $y = 2$ , and $z = -5$ :

x^2 - \frac{y^3 z}{|x + z|}

Fill in the blanks with the correct numerical values.

Aşağıdaki boşlukları doldurun

The evaluated value of the fraction term alone (i.e.,

\frac{y^3 z}{|x + z|}

) is , which makes the final value of the entire expression equal to .

Cevabı ve açıklamayı göster

Cevap

The fraction term evaluates to -5, and the final expression evaluates to 14.

By following the order of operations (PEMDAS), we first substitute the values and handle operations inside grouping symbols like absolute value (

|-3 + -5| = 8

). Next, exponents are calculated (

(-3)^2 = 9

and

2^3 = 8

), followed by multiplication and division to simplify the fraction to

-5

. Finally, subtracting this negative value gives

9 - (-5) = 14

.

Adım Adım Çözüm

1

Substitute the given values into the expression.

(-3)^2 - \frac{2^3(-5)}{|-3 + (-5)|}

Direct variable substitution according to the given values is the first step in evaluating any algebraic expression.

2

Evaluate the numerator of the fraction.

2^3(-5) = 8(-5) = -40

According to the order of operations, exponents must be evaluated before multiplication.

3

Evaluate the denominator of the fraction.

|-3 + (-5)| = |-8| = 8

Grouping symbols, such as absolute value bars, must be evaluated from the inside out.

4

Divide the numerator by the denominator to find the fraction term's value.

\frac{-40}{8} = -5

Division within the fraction is performed before interacting with the rest of the expression.

5

Evaluate the squared term and subtract the fraction's value.

9 - (-5) = 9 + 5 = 14

Exponents are evaluated first, and subtracting a negative number is mathematically equivalent to adding a positive number.

Anahtar Kavram

Evaluating multi-step algebraic expressions involving negative bases, absolute values, and fractions.

Tahmini Süre:1m 0s

Soru 4891Soru →

The sum of three consecutive negative even integers is $-102$ . What is the absolute value of the smallest of these integers?

Cevabı ve açıklamayı göster

Cevap: 36

Cevap

36

By defining the consecutive even integers algebraically, the smallest integer is correctly identified as

-36

. Taking the absolute value of

-36

yields

36

.

Adım Adım Çözüm

1

Define variables for the three consecutive even integers.

Let the smallest integer be

x

. The next consecutive even integers are

x + 2

and

x + 4

.

Consecutive even integers are always 2 units apart.

2

Set up the equation.

x + (x + 2) + (x + 4) = -102

The sum of the three integers is given as

-102

.

3

Solve for

x

.

3x + 6 = -102

leads to

3x = -108

, yielding

x = -36

.

Isolating

x

provides the value of the smallest integer.

4

Calculate the absolute value.

|-36| = 36

The question specifically asks for the absolute value of the smallest integer.

Anahtar Kavram

Consecutive integers and absolute value properties

Soru 4892Soru →

Find the value of the following expression for $x = -3$ , $y = -2$ , and $z = \frac{1}{2}$ :

\frac{x^2 y - y^3}{x - y} + 4z

Cevabı ve açıklamayı göster

Cevap: 12

Cevap

12

The correct result of 12 is obtained by substituting the given values, correctly applying exponents to negative bases, properly combining terms with double negatives, and following the standard order of operations.

Adım Adım Çözüm

1

Substitute the values of x, y, and z into the algebraic expression.

\frac{(-3)^2(-2) - (-2)^3}{(-3) - (-2)} + 4(\frac{1}{2})

Direct substitution establishes the numerical expression to be evaluated.

2

Evaluate the terms containing exponents.

(-3)^2 = 9

and

(-2)^3 = -8

Following the order of operations, exponents are calculated before multiplication or addition.

3

Multiply the factors in the numerator and the separate z-term.

The numerator term becomes

9(-2) = -18

. The z-term becomes

4(\frac{1}{2}) = 2

.

Multiplication is the next step in simplifying the expression according to the order of operations.

4

Simplify the fraction's numerator and denominator by performing the subtractions.

Numerator:

-18 - (-8) = -10

. Denominator:

-3 - (-2) = -1

.

The fraction bar acts as a grouping symbol; the numerator and denominator must be simplified completely before division.

5

Divide the simplified numerator by the simplified denominator.

\frac{-10}{-1} = 10

Completing the division of the rational part of the expression.

6

Add the result of the division to the remaining term.

10 + 2 = 12

Addition is the final operation required to find the total value.

Anahtar Kavram

Evaluating complex algebraic expressions using substitution and the order of operations with negative integers and fractions.

Soru 4893Soru →

A logistics coordinator is planning a delivery route using a regional highway map. The map's legend indicates a scale of $0.4\text{ inches} = 15\text{ miles}$ . If the distance between the distribution center and the final delivery point measures $6.2\text{ inches}$ on the map, what is the actual driving distance between the two locations?

23.25\text{ miles}

37.2\text{ miles}

93\text{ miles}

232.5\text{ miles}

Cevabı ve açıklamayı göster

Cevap: $232.5\text{ miles}$

Cevap

The actual driving distance is

232.5\text{ miles}

.

The correct actual distance is

232.5\text{ miles}

. To solve this, find the number of

0.4

-inch units in

6.2\text{ inches}

by dividing:

6.2 \div 0.4 = 15.5

. Then, multiply this factor by the

15\text{ miles}

that each unit represents:

15.5 \times 15 = 232.5\text{ miles}

. Alternatively, finding the unit rate of

37.5\text{ miles per inch}

(

15 \div 0.4

) and multiplying by

6.2\text{ inches}

yields the same correct result.

Adım Adım Çözüm

1

Determine the unit scale (actual miles per inch on the map).

15 \div 0.4 = 37.5\text{ miles per inch}

This establishes a baseline multiplier to convert any map measurement into real-world miles.

2

Calculate the actual driving distance.

6.2 \times 37.5 = 232.5\text{ miles}

Scaling up the measured map distance by the unit rate yields the total actual distance.

Anahtar Kavram

Scale Drawings and Map Measurements

Tahmini Süre:1m 30s

Soru 4894Soru →

A carpenter is cutting a wooden board that is initially $12 \frac{1}{2}$ feet long. First, he cuts off a piece that is $3 \frac{3}{4}$ feet long and sets it aside. Then, he divides the remaining board into $5$ equal sections. What is the length of each of these $5$ sections?

11 \frac{3}{4}

feet

1

foot

1 \frac{3}{4}

feet

2 \frac{1}{20}

feet

Cevabı ve açıklamayı göster

Cevap: $1 \frac{3}{4}$ feet

Cevap

Each of the

5

sections has a length of

1 \frac{3}{4}

feet.

The correct sequence of operations is to first determine the remaining length by subtracting

3 \frac{3}{4}

from

12 \frac{1}{2}

, yielding

8 \frac{3}{4}

feet. Then, dividing this remaining length by

5

results in

1 \frac{3}{4}

feet per section.

Adım Adım Çözüm

1

Calculate the length of the remaining board by subtracting the cut piece from the total length.

12 \frac{1}{2} - 3 \frac{3}{4}

The carpenter first removes a piece, leaving a smaller board to be divided.

2

Find a common denominator to perform the subtraction.

12 \frac{2}{4} - 3 \frac{3}{4}

Fractions must have the same denominator to be subtracted.

3

Borrow from the whole number to subtract the fractions.

11 \frac{6}{4} - 3 \frac{3}{4} = 8 \frac{3}{4}

feet

Since

\frac{2}{4}

is less than

\frac{3}{4}

, one whole unit must be converted into

\frac{4}{4}

.

4

Divide the remaining length by 5 to find the length of each section.

8 \frac{3}{4} \div 5

The remaining board is split into 5 equal parts.

5

Convert the mixed number to an improper fraction and multiply by the reciprocal of 5.

\frac{35}{4} \times \frac{1}{5} = \frac{7}{4} = 1 \frac{3}{4}

feet

Division by a whole number is equivalent to multiplying by its reciprocal.

Anahtar Kavram

Solving multi-step problems involving subtraction and division of mixed numbers with unlike denominators.

Soru 4895Soru →

An ammunition crate contains tracer rounds and standard rounds in a ratio of $5:12$ . If the crate holds a total of $510$ rounds, how many tracer rounds does it contain?

Cevabı ve açıklamayı göster

Cevap: 150; 150 rounds; 150 tracer rounds

Cevap

150

By adding the ratio parts (

5 + 12 = 17

), we find that tracer rounds make up

\frac{5}{17}

of the total contents. Multiplying the total number of rounds (

510

) by this fraction yields

150

tracer rounds.

Adım Adım Çözüm

1

Calculate the total number of parts in the ratio.

5 + 12 = 17

total parts.

The total quantity of rounds (

510

) corresponds to the combined parts of the ratio.

2

Determine the number of rounds represented by a single part.

510 \div 17 = 30

rounds per part.

Dividing the total items by the total parts finds the scale factor.

3

Calculate the total number of tracer rounds.

5 \times 30 = 150

tracer rounds.

The ratio states there are

5

parts of tracer rounds, so we multiply the scale factor by

5

.

Anahtar Kavram

Solving part-to-whole problems using a part-to-part ratio.

Soru 4896Soru →

A maintenance crew uses $2$ gallons of primer for every $5$ gallons of paint. If the crew uses $10$ gallons of primer, how many gallons of paint are needed?

Cevabı ve açıklamayı göster

Cevap: 25; 25 gallons; 25 gal

Cevap

25

The given ratio of primer to paint is

2:5

. Since

10

gallons of primer is

5

times the original

2

gallons, you must also multiply the

5

gallons of paint by

5

to maintain the ratio. Therefore,

5 \times 5 = 25

gallons of paint are needed.

Adım Adım Çözüm

1

Set up a proportion using the given ratio of primer to paint.

\frac{2}{5} = \frac{10}{x}

To relate the base ratio to the actual amounts used, where

x

represents the unknown gallons of paint.

2

Solve the proportion for

x

.

x = \frac{5 \times 10}{2} = 25

Using cross-multiplication isolates

x

to find the required amount of paint.

Anahtar Kavram

Solving direct proportions

Soru 4897Soru →

Arrange the following fractions and mixed numbers in ascending order (from least to greatest).

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

The correct ascending order is

2 \frac{7}{12}

,

2 \frac{5}{8}

,

\frac{8}{3}

, and

\frac{11}{4}

.

By converting all values to mixed numbers with a common denominator of 24, we find their fractional parts are

\frac{14}{24}

,

\frac{15}{24}

,

\frac{16}{24}

, and

\frac{18}{24}

. Because all whole numbers are 2, the order of the original fractions matches the ascending order of these fractional parts.

Adım Adım Çözüm

1

Convert the improper fractions to mixed numbers to simplify comparison.

\frac{11}{4} = 2 \frac{3}{4}

and

\frac{8}{3} = 2 \frac{2}{3}

. The other numbers are already mixed numbers:

2 \frac{5}{8}

and

2 \frac{7}{12}

.

Because all the whole numbers are 2, we only need to compare their fractional parts to determine the order.

2

Identify the least common denominator (LCD) for the fractional parts:

\frac{3}{4}

,

\frac{5}{8}

,

\frac{7}{12}

, and

\frac{2}{3}

.

The denominators are 4, 8, 12, and 3. The lowest number they all divide into evenly is 24.

A common denominator is required to accurately compare the sizes of fractions with unlike denominators.

3

Convert each fractional part to an equivalent fraction with a denominator of 24.

\frac{3}{4} = \frac{18}{24}

,

\frac{5}{8} = \frac{15}{24}

,

\frac{7}{12} = \frac{14}{24}

, and

\frac{2}{3} = \frac{16}{24}

.

Multiplying both the numerator and denominator by the same value preserves the fraction's overall mathematical value.

4

Order the converted fractions from least to greatest based on their numerators.

\frac{14}{24} < \frac{15}{24} < \frac{16}{24} < \frac{18}{24}

.

When denominators are equal, a larger numerator represents a larger overall value.

5

Match the ordered fractions back to their original given forms.

2 \frac{7}{12}

(from

\frac{14}{24}

),

2 \frac{5}{8}

(from

\frac{15}{24}

),

\frac{8}{3}

(from

\frac{16}{24}

), and

\frac{11}{4}

(from

\frac{18}{24}

).

The final answer must present the exact numbers provided in the original stem.

Anahtar Kavram

Comparing and Ordering Fractions with Unlike Denominators

Soru 4898Soru →

During cold-weather evaluation of an expeditionary filtration unit, technicians recorded the following observations:

• While the secondary filter cartridge was porous, the primary silicone membrane proved completely impermeable.
• Thermal fluctuations caused only a transient drop in line pressure, whereas the baseline operating pressure remained enduring and constant.
• In contrast to the sluggish motorized exhaust valve, the pneumatic relief flap exhibited an instantaneous, rapid release.
• Despite the pungent odor emitted by the solvent wash, the neutralizing rinse was entirely mild and odorless.

Based on the contrast context clues in the passage, match each bolded word to its correct meaning.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

Porous matches 'Permeable and allowing fluids to pass through'; Transient matches 'Temporary and lasting for only a short period'; Sluggish matches 'Slow-moving and delayed in action'; Pungent matches 'Sharp, intense, and biting in smell'.

Each match correctly inverts the stated antonym clue signaled by the transition words: 'porous' is the opposite of impermeable (permeable), 'transient' is the opposite of enduring (temporary), 'sluggish' is the opposite of instantaneous/rapid (slow-moving), and 'pungent' is the opposite of mild/odorless (sharp and intense).

Adım Adım Çözüm

1

Identify the contrast signal words in each observation sentence.

Signal words identified: 'While', 'whereas', 'In contrast to', and 'Despite'.

Contrast signal words establish that the target bolded term has the opposite meaning of the descriptive clue provided in the same sentence.

2

Locate the contrasting counterpart words for each target term.

Porous opposes 'impermeable'; Transient opposes 'enduring and constant'; Sluggish opposes 'instantaneous, rapid'; Pungent opposes 'mild and odorless'.

Extracting the explicit antonym in the text defines the boundary of the unknown word's meaning.

3

Match each bolded term to the definition representing the opposite of its textual counterpart.

Porous = permeable; Transient = temporary; Sluggish = slow-moving; Pungent = sharp/intense in smell.

Inverting the contrasting clues produces the precise contextual definitions.

Anahtar Kavram

Using explicit contrast signal words and antonymous counterparts to infer vocabulary definitions in technical context

Tahmini Süre:1m 15s

Soru 4899Soru →

A carpenter has a wooden board that is $5 \frac{3}{4}$ inches wide. If he shaves off exactly $\frac{1}{8}$ of an inch from the width, what is the new width of the board?

5 \frac{5}{8}

inches

5 \frac{1}{2}

inches

5 \frac{7}{8}

inches

5 \frac{1}{4}

inches

Cevabı ve açıklamayı göster

Cevap: $5 \frac{5}{8}$ inches

Cevap

The new width of the board is

5 \frac{5}{8}

inches.

To find the new width, subtract the shaved amount from the original width:

5 \frac{3}{4} - \frac{1}{8}

. First, find a common denominator, which is 8. Convert

\frac{3}{4}

to

\frac{6}{8}

. Subtracting

\frac{1}{8}

from

5 \frac{6}{8}

gives the correct answer of

5 \frac{5}{8}

inches.

Adım Adım Çözüm

1

Set up the subtraction problem based on the context.

5 \frac{3}{4} - \frac{1}{8}

The phrase 'shaves off' indicates subtraction from the original width.

2

Find a common denominator for the fractions

\frac{3}{4}

and

\frac{1}{8}

.

The common denominator is

8

.

Fractions must have the same denominator before they can be subtracted.

3

Convert

\frac{3}{4}

to an equivalent fraction with a denominator of

8

.

\frac{3 \times 2}{4 \times 2} = \frac{6}{8}

Multiplying both the numerator and denominator by

2

keeps the fraction's value the same while converting the denominator.

4

Subtract the fractions.

5 \frac{6}{8} - \frac{1}{8} = 5 \frac{5}{8}

Subtract the numerators while keeping the common denominator the same.

Anahtar Kavram

Subtracting mixed numbers with unlike denominators

Soru 4900Soru →

Which of the following statements about integers is always true?

The difference between any integer and its absolute value is always an even integer.

The product of any non-zero integer and its absolute value is always a positive integer.

Subtracting a negative integer from its absolute value always results in zero.

The sum of any negative integer and its absolute value is always a negative integer.

Cevabı ve açıklamayı göster

Cevap: The difference between any integer and its absolute value is always an even integer.

Cevap

The statement claiming that the difference between any integer and its absolute value is always an even integer.

For any non-negative integer, the difference between the integer and its absolute value is 0, which is an even integer. For any negative integer, the difference evaluates to twice the integer (2x), which is a multiple of 2 and therefore also even. Thus, the statement holds true for all integers.

Adım Adım Çözüm

1

Analyze the behavior of the expression (x - |x|) for non-negative integers.

If x is 0 or positive, |x| = x. Therefore, x - |x| = x - x = 0.

To test the property for the first distinct category of integers.

2

Analyze the behavior of the expression (x - |x|) for negative integers.

If x is negative, |x| = -x. Therefore, x - |x| = x - (-x) = x + x = 2x.

To test the property for the remaining category of integers.

3

Determine the parity (odd/even status) of the results from the previous steps.

The number 0 is an even integer. The expression 2x is inherently a multiple of 2, making it an even integer regardless of the value of x.

To conclude whether the difference is universally even.

Anahtar Kavram

Parity and Absolute Value Properties

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Sık Yapılan Hatalar

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